Grades 6-8 — Problem-Solving Talks
Professional learning and Instructional Resources for Math Support and Intervention
Review fraction and decimal concepts from grades 3-5.
Then, apply those concepts to Preview foundational grades 6-8 strategies and concepts for representing rational numbers and solving proportional problems.
Conceptual Overview of Problem-Solving Talks
Problem-Solving Talks Review Grades 3-5 strategies and concepts for representing whole numbers, fractions, and decimals on number lines.
Then, students are challenged to apply those grades 3-5 strategies to Preview Foundational Grades 6-8 representations, strategies, and concepts.
Strategies to represent whole numbers are applied to represent integers.
Strategies to represent fractions and decimals are applied to represent negative rational numbers.
Foundational ratio strategies are previewed and applied to generate equivalent ratios and solve problems.
Strategies to represent rational numbers on number lines are applied to represent rates on double number lines and percents on percent bars.
Problem-Solving Talks
Overview of Instructional and Professional Learning Resources
Overview of Problem-Solving Talks
Problem-Solving Talks are designed to review grades 3-5 concepts involving fractions, decimals, and computation while previewing foundational grade 6-8 representations and strategies for rational numbers, ratios, rates, and percents. These resources help teachers to connect review topics, such as locating and labeling fractions and decimals on number lines, directly to essential grade 6 strategies and concepts, such as representing negative rational numbers or equivalent fractions, decimals, and percents on a percent bar.
These resources are built around videos that structure a problem-solving talk with a class or small group of students. The video briefly reviews essential representations, strategies, and concepts. Then, the group or class of students completes a set of problem-solving challenges where they build representations and solve problems using a set of magnetic manipulatives on a whiteboard. Instructional notes for the video help teachers focus their questioning strategies and identify pause points in the video to address diagram comprehension, concept development, and vocabulary. Finally, students apply what they have learned through daily problem-solving tasks and practice pages.
Problem-Solving Videos
Structure a Problem-Solving Talk
Sample PS Video — Measure to Plot and Label Positive and Negative Fractions
Problem-Solving Talks review essential concepts from grades 3-5 and preview representations and strategies from grades 6-8.
Problem-Solving Videos structure these talks by reviewing or introducing essential representations or strategies and challenging groups of students to build representations and solve problems.
For example, many students entering middle school have a weak understanding of how measurement is used to locate and label whole numbers, fractions, and decimals on number lines. The sequence of PPS Videos starts with a review of plotting whole numbers, fractions, and decimals on number lines. Then, students apply these strategies to locate and label negative integers, fractions, and decimals.
Resources for Problem-Solving Talks include a magnetic manipulative kit for whiteboards, instructional notes, application tasks, and practice pages.
Problem Solving Videos are structured to:
Review and Preview essential representations, strategies, and concepts
Each Problem-Solving Video reviews essential concepts from previous grades or videos and then applies those concepts to preview foundational grade-level representations or strategies.
Challenge a small group or class of students to build representations and solve problems
Each Problem-Solving Video includes a series of problem-solving Challenges that are solved as a small group or class. Students use manipulatives from the Magnetic Manipulative Kit for whiteboards to apply strategies demonstrated in the video.
REVIEW — The length of a unit-fraction bar is defined by the number of equal-length bars that measure a length of 1 on the number line. So, the denominator of a fraction can be idenified as the number of equal length bars that measrue from zero to 1 on a number line.
REVIEW — Unit fraction bars are used to measure to the right of zero to plot and label fractions. With unit fraction bars on number lines, the number of unit fraction bars is the numerator of the fraction.
CHALLENGE — Students in the small group or class are challenged to use the magnetic measurement bars on a whiteboard to measure, plot, and label fractions. This is an opportunity to point out to students that measuring fractions greater than one with unit fraction bars follows the same rules as measuring fractions between 0 and 1.
REVIEW — Two numbers that measure the same distance and direction from zero on a number line are said to be equivalent. This example demonstrates the equivalence of a whole number and a fraction. In subsequent Problem Solving Talks, this concept will be applied to demonstrate equivalent fractions and decimals.
0:17
0:23
0:55
1:19
2:00
2:08
2:33
REVIEW — Students use a fraction strip to skip count by fractions that are equivalent to whole numbers. Then, the add additional unit fractions bars to measure to fractions between whole numbers.
2:47
3:00
CHALLENGE — Students use magnetic fraction strips and measurement bars to label existing points on a number line.
PREVIEW — Unit fraction bars measure to negative fractions to the left of zero using the same use rules as measuring positive fractions to the right of zero.
CHALLENGE — Students use magnetic fraction strips and measurement bars to measure, plot, and label negative fractions to the left of zero.
3:25
PREVIEW — Negative fractions are introduced as the reflection of a positive fraction across zero.
CHALLENGE — Students identify the length of a new set of unit fraction bars. Then, they use fraction strips and unit fraction bars to label existing points that represent negative fractions.
Magnetic Whiteboard Manipulative Kit
Challenge Students to Build Representations and Solve Problems
Magnetic Number Line Segments, Measurement Bars, and Fraction Strips
Drawn to scale on a 48 in by 36 in magnetic whiteboard.
Magnetic Grid and Chips, Double Number Lines, and Percent Bars
Drawn to scale on a 48 in by 36 in magnetic whiteboard.
The Video Overview and Instructional Notes outline the conceptual highlights of the Problem-Solving Videos and list the essential strategies and concepts that are introduced and reviewed. In addition, video pause points with instructional notes identify important representations, strategies, and concepts and offer suggestions for facilitating discussions and problem-solving with students.
The instructional notes offer questioning strategies for each Problem-Solving Challenge and identify other pause points with notes on:
Diagram Comprehension
Essential Concept Development
Vocabulary Discussion
Problem-Solving
Video Overview and Instructional Notes
Develop and Refine Questioning Strategies
REVIEW Pause Points
The first three pages of this VOIN review the basics for measuring to locate and label fractions on number lines.
Identify unit fractions bars
Measure to fractions less than and greater than one.
Identify equivalent fractions and whole numbers that measure from zero to the same point on the line.
PREVIEW Pause Points
The Preview pause points on this page challenge students to apply the measurement strategies to plot and label negative fractions to the left of zero.
The mirror image of a positive fraction across zero is the opposite negative fraction.
Negative fractions measure a distance to the left of zero, where measurement bars represent distance and the arrows (or vectors) represent both distance and direction from zero.
Then, students are Challenged to use magnetic measurement bars and fraction strips to locate and label negative fractions on a whiteboard number line.
